Assigning the priors

As we know, the priors are ingested by the MCMC algorithm, and are used to calculate the posterior densities. But how should the priors be assigned? Do we actually need a prior for each parameter?

Defining the support

Priors are just statistical distributions that reflect the initial expectation that the modeler has about each parameter. The very first thing we need to decide is, what is the support for the corresponding distributions? For example, for most coefficients in a linear regression model, the modeler very likely knows the correct sign for them. When modeling sales of a product in terms of its price and a promotional effect, the price effect should be negative (a higher price = less sales), and...